SOLUTION: what is the solution set for the quadratic equation x^2+6x-3=0?

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Question 392966: what is the solution set for the quadratic equation x^2+6x-3=0?
Answer by jim_thompson5910(28598) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x-3=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x-3 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=-3


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=-3


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


x+=+%28-6+%2B-+sqrt%28+36%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--12%29 as sqrt%2836%2B12%29


x+=+%28-6+%2B-+sqrt%28+48+%29%29%2F%282%281%29%29 Add 36 to 12 to get 48


x+=+%28-6+%2B-+sqrt%28+48+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+4%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%284%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+2%2Asqrt%283%29 Reduce.


x+=+-3%2B2%2Asqrt%283%29 or x+=+-3-2%2Asqrt%283%29 Break up the expression.


So the solutions are x+=+-3%2B2%2Asqrt%283%29 or x+=+-3-2%2Asqrt%283%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim